Clean and efficient loop fusion for all your iterating needs!
# #require "iter";;
# let p x = x mod 5 = 0 in
Iter.(1 -- 5_000 |> filter p |> map (fun x -> x * x) |> fold (+) 0);;
- : int = 8345837500
Iter
is a simple abstraction over iter
functions
intended to iterate efficiently
on collections while performing some transformations.
Common operations supported by Iter
include
filter
, map
, take
, drop
, append
, flat_map
, etc.
Iter
is not designed to be as general-purpose or flexible as Seq
.
Rather, it aims at providing a very simple and efficient
way of iterating on a finite number of values, only allocating (most of the time)
one intermediate closure to do so. For instance, iterating on keys, or values,
of a Hashtbl.t
, without creating a list.
Similarly, the code above is turned into a single optimized
for loop with flambda
.
There is only one important type, 'a Iter.t
, and lots of functions built
around this type.
See the online API
for more details on the set of available functions.
Some examples can be found below.
The library used to be called Sequence
.
Some historical perspective is provided
in this talk
given by @c-cube at some OCaml meeting.
Conversion between n container types
would take n² functions. In practice, for a given collection
we can at best hope for to_list
and of_list
.
With iter, if the source structure provides a
iter
function (or a to_iter
wrapper), it becomes:
# let q : int Queue.t = Queue.create();;
val q : int Queue.t = <abstr>
# Iter.( 1 -- 10 |> to_queue q);;
- : unit = ()
# Iter.of_queue q |> Iter.to_list ;;
- : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
# let s : int Stack.t = Stack.create();;
val s : int Stack.t = <abstr>
# Iter.(of_queue q |> to_stack s);;
- : unit = ()
# Iter.of_stack s |> Iter.to_list ;;
- : int list = [10; 9; 8; 7; 6; 5; 4; 3; 2; 1]
Note how the list of elements is reversed when we transfer them from the queue to the stack.
Another example is extracting the list of values of a hashtable (in an undefined order that depends on the underlying hash function):
# let h: (int, string) Hashtbl.t = Hashtbl.create 16;;
val h : (int, string) Hashtbl.t = <abstr>
# for i = 0 to 10 do
Hashtbl.add h i (string_of_int i)
done;;
- : unit = ()
# Hashtbl.length h;;
- : int = 11
# (* now to get the values *)
Iter.of_hashtbl h |> Iter.map snd |> Iter.to_list;;
- : string list = ["6"; "2"; "8"; "7"; "3"; "5"; "4"; "9"; "0"; "10"; "1"]
for
loopsThe for
loop is a bit limited, and lacks compositionality.
Instead, it can be more convenient and readable to
use Iter.(--) : int -> int -> int Iter.t
.
# Iter.(1 -- 10_000_000 |> fold (+) 0);;
- : int = 50000005000000
# let p x = x mod 5 = 0 in
Iter.(1 -- 5_000
|> filter p
|> map (fun x -> x * x)
|> fold (+) 0
);;
- : int = 8345837500
NOTE: with flambda under sufficiently strong optimization flags, such compositions of operators should be compiled to an actual loop with no overhead!
A small λ-calculus AST, and some operations on it.
# type term =
| Var of string
| App of term * term
| Lambda of term ;;
type term = Var of string | App of term * term | Lambda of term
# let rec subterms : term -> term Iter.t =
fun t ->
let open Iter.Infix in
Iter.cons t
(match t with
| Var _ -> Iter.empty
| Lambda u -> subterms u
| App (a,b) ->
Iter.append (subterms a) (subterms b))
;;
val subterms : term -> term Iter.t = <fun>
# (* Now we can define many other functions easily! *)
let vars t =
Iter.filter_map
(function Var s -> Some s | _ -> None)
(subterms t) ;;
val vars : term -> string Iter.t = <fun>
# let size t = Iter.length (subterms t) ;;
val size : term -> int = <fun>
# let vars_list l = Iter.(of_list l |> flat_map vars);;
val vars_list : term list -> string Iter.t = <fun>
Makes it easy to write backtracking code (a non-deterministic
function returning several 'a
will just return a 'a Iter.t
).
Here, we generate all permutations of a list by
enumerating the ways we can insert an element in a list.
# open Iter.Infix;;
# let rec insert x l = match l with
| [] -> Iter.return [x]
| y :: tl ->
Iter.append
(insert x tl >|= fun tl' -> y :: tl')
(Iter.return (x :: l)) ;;
val insert : 'a -> 'a list -> 'a list Iter.t = <fun>
# let rec permute l = match l with
| [] -> Iter.return []
| x :: tl -> permute tl >>= insert x ;;
val permute : 'a list -> 'a list Iter.t = <fun>
# permute [1;2;3;4] |> Iter.take 2 |> Iter.to_list ;;
- : int list list = [[4; 3; 2; 1]; [4; 3; 1; 2]]
The module examples/sexpr.mli
exposes the interface of the S-expression
example library. It requires OCaml>=4.0 to compile, because of the GADT
structure used in the monadic parser combinators part of examples/sexpr.ml
.
Be careful that this is quite obscure.
Seq
from the standard library, and with Gen
Seq
is an external iterator.
It means that the code which consumes
some iterator of type 'a Seq.t
is the one which decides when to
go to the next element. This gives a lot of flexibility, for example
when iterating on several iterators at the same time:
let rec zip a b () = match a(), b() with
| Nil, _
| _, Nil -> Nil
| Cons (x, a'), Cons (y, b') -> Cons ((x,y), zip a' b')
Iter
is an internal iterator. When one wishes to iterate over
an 'a Iter.t
, one has to give a callback f : 'a -> unit
that is called in succession over every element of the iterator.
Control is not handed back to the caller before the whole iteration is over.
This makes zip
impossible to implement. However, the type 'a Iter.t
is general enough that it can be extracted from any classic iter
function,
including from data structures such as Map.S.t
or Set.S.t
or Hashtbl.t
;
one cannot obtain a 'a Seq.t
from these without having access to the internal
data structure.
Gen
(from the gen library)
is an external iterator, like Seq
, but it is imperative, mutable, and consumable
(you can't iterate twice on the same 'a Gen.t
).
It looks a lot like iterators in rust/java/… and can be pretty efficient in some cases.
Since you control iteration you can also write map2
, for_all2
, etc but
only with linear use of input generators (since you can traverse them only once).
That requires some trickery for cartesian_product (like storing already produced elements internally).
In short, 'a Seq.t
is more expressive than 'a Iter.t
, but it also
requires more knowledge of the underlying source of items.
For some operations such as map
or flat_map
, Iter is also extremely
efficient and will, if flambda permits, be totally removed at
compile time (e.g. Iter.(--)
becomes a for loop, and Iter.filter
becomes a if test).
For more details, you can read http://gallium.inria.fr/blog/generators-iterators-control-and-continuations/ or
see the slides about Iter
by me (c-cube) when Iter
was still called Sequence
.
opam install iter
make all install
If you have qtest installed, you can build and run tests with
$ make test
If you have benchmarks installed, you can build and run benchmarks with
$ make benchs
To see how to use the library, check the following tutorial.
The tests
and examples
directories also have some examples, but they're a bit arcane.
Iter is available under the BSD license.